Method and apparatus for determining a pulmonary function parameter for gas exchange

ABSTRACT

A method and apparatus for determining a pulmonary function parameter, EVG, indicative of a living subject&#39;s effective lung volume, namely the lung volume in which gas exchange between respiratory air and pulmonary blood takes place efficiently. The apparatus carries out the steps of the method: (1) determining for a first breath during normal steady state breathing of the subject the end-tidal carbon dioxide or oxygen concentration P et1  and the average rate of flow V a1 , over the duration T 1  of the breath, of expired carbon dioxide or oxygen, (2) determining for a second breath comprising a breath-hold period the end-tidal carbon dioxide or oxygen concentration P et2  and the average rate of flow V a2 , over the duration T 2  of the breath, of expired carbon dioxide or oxygen, and (3) determining EVG as a quantity proportional to the ratio of the difference between said average flow rates V a1  and V a2  to the difference between said end-tidal concentrations P et2  and P et1 .

CROSS REFERENCE TO RELATED APPLICATION

The present application is the national stage under 35 U.S.C. 371 ofPCT/SE98/02055, filed Nov. 13 1998.

This invention relates to a method and apparatus for determining apulmonary function parameter, here abbreviated EVG, which is indicativeof a living subject's effective lung volume, that is, the volume of thepart-of the lungs which participates efficiently in the gas exchangebetween the respiratory gas and the pulmonary blood.

When a person is breathing spontaneously or is connected to an apparatusthat provides artificial respiration, the ventilation of the lungs ischaracterised by the volume of the inspired gas, the so called tidalvolume VT, and the breathing rate.

However, all of the gas making up the VT does not reach the fineststructures, the alveoli, of the lungs where the exchange of gases takesplace (oxygen being taken up by the pulmonary blood and carbon dioxidebeing released from the pulmonary blood into the gas phase). Moreover,part of VT gas may reach unperfused parts of the lungs and so will beunutilized because this part of the VT gas will have no contact with thepulmonary blood consequently will not take part in the gas-exchangeprocess.

An important therapeutic goal in modern clinical care is to arrange forthe best possible conditions for gas exchange in the lungs. The presentinvention addresses the problem how to assess the efficiency of the gasexchange. According to the invention an apparatus and a method areprovided to measure this efficiency and a measure of the matching ofventilation with perfusion is given that can be used to guide therapy.

That portion of the VT gas which does not take part in the gas exchangeprocess is called the dead space volume, VD, and the ratio of the deadspace volume to the tidal volume is called the VD:VT fraction. The VD:VTfraction is routinely estimated in the clinical setting usingmeasurements of the carbon dioxide partial pressures of the expired gasand the arterial blood. A description of the state of the art and ahistorical review of these methods are found in R. Fletcher “The singlebreath test for carbon dioxide” (1980) Thesis University of LundDepartment of Anaesthesia and Clinical Physiology, Lund, Sweden.However, these methods are less than satisfactory because they rely onlyon measurements of carbon dioxide partial pressure and cannot thereforetake into account the effects of both ventilation and circulation in thelungs. Methods based on the calculation of the VD:VT fraction thereforeare not specific enough to guide therapy.

An alternative technique for estimating the effectiveness of the gasexchange process is to determine the fraction of the lung volume thatparticipates fully in the gas-exchange process. Since carbon dioxide issoluble in lung tissue, the total volume of carbon dioxide in the lungsis made up of three parts, the gas volume in the alveoli of the lungs,V_(g), and the gas volumes dissolved in the lung tissue, V_(t), and inthe pulmonary blood, V_(b), respectively. The total volume is called theequivalent lung volume for carbon dioxide, abbreviated ELV, and can beestimated using carbon dioxide rebreathing techniques. (A Dubois: JApplied Physiology 5, 1, 1952; M Winsborough et al: Clinical Science58,263 1980).

Although this approach does not have the same limitations as the VD:VTfraction techniques, the equivalent lung volume concept does not providea sensitive measure of the effectiveness of the gas exchange process.This is so because of the inevitable gas mixing that takes place in thelungs of a person who breathes back and forth. This gas mixing tends todiminish the distinction between effective and ineffective lung areas.(M Petrini et al: J Appl. Phys. 53(4) 930 1982). In addition, theresulting distortion of information depends on the characteristics ofthe breathing pattern and/or the conditions of the rebreathing setup.Both systematic and random errors of measurement are introduced in thisway.

The present invention provides a solution to these problems whereby asensitive and specific assessment of the effective gas exchange volumein the lungs is possible. In addition, the measurement is simple andquick and can be performed non-invasively.

The invention will be fully understood from the following descriptionwith reference to the accompanying drawings.

FIG. 1 is a schematic view showing a patient who breathes with the aidof a ventilator;

FIGS. 2a and 2 b are diagrams illustrating the method according to theinvention and showing gas flow and concentration versus time for anormal breath (FIG. 2b) and a breath comprising a breath-hold period(FIG. 2b);

FIGS. 3a, 3 b, 3 c and 3 d are four diagrams illustrating use of themethod according to the invention as a guide for therapy.

FIG. 4 is a diagram showing how pulmonary tissue volume can bedetermined using the method according to the invention.

Referring to FIG. 1, a patient P is breathing spontaneously or with theaid of a ventilator V through an inspiratory breathing line J and anexpiratory breathing line E. A standard fast-response carbon dioxideanalyzer A (e.g. Capnomac AGM-103, Datex Instrumentarium Inc. Finland)is placed between the patient and the point Y where the inspiratory andexpiratory lines meet. A flowmeter F, which may be a part of theventilator (e.g. Servo Ventilator 900B), is placed in the expiratorybreathing line to continuously record the expiratory flow from thepatient. A data processing unit D collects the signal from the analyzerA and the flowmeter F and calculates the amount of carbon dioxideexpired with each breath, TVCO2 [ml]. This is done by integration overtime of the signal from the analyzer A and the flow signal from theflowmeter F. Typical graphs showing the flow of respiratory gas over asingle normal breath and a breath comprising a breath-hold period areshown in FIGS. 2a and 2 b.

In addition to the TVCO2 value, unit D also determines the end-tidal CO₂concentration value, P_(et) [%], that is, the carbon dioxide partialpressure measured at the very end of the expiration. This value is anindication of the carbon dioxide concentration as close to the blood-gasbarrier as is possible using noninvasive means.

A specific example will illustrate the novel method.

The patient is breathing regularly at a rate of 15 breaths per minute,so that the duration of each breath is T₁=4 seconds.

Then the patient is caused to hold his breath for a short time T_(b)after the end of the inspiratory phase of a breath to be observed, T_(b)being 3 seconds, for example. If the patient is breathing with the aidof the ventilator V, the pause time between inspiration and expirationset on the ventilator (typically 0.25×T₁ seconds) is increased in onebreath by T_(b) seconds (meaning in this example increased from 1 secondto 4 seconds) so that the desired breath-hold period is implemented andthe duration of the breath is extended to T₂=7 seconds. If the patientbreathes spontaneously, the breath-hold period can be implemented simplyby the patient holding his breath for the required time. After thissingle breath-hold manoeuvre the normal respiration pattern is resumed.

FIG. 2a shows typical respiratory flow patterns during normal breathing.FIG. 2b shows the corresponding conditions during the breath whichcomprises the breath-hold period.

The following typical values are obtained from unit D:

Normal breath: TVCO2₁=12 ml; P_(et1)=5.0%

Breath-hold breath: TVCO2₂=14 ml; P_(et2)=5.5%

In steady state breathing, that is, when the carbon dioxide leaving thepulmonary blood equals the expired carbon dioxide, the continuous carbondioxide inflow from the pulmonary blood into the lungs thus isTVCO2₁:T₁=12:4=3 ml CO₂/s.

However, the expired carbon dioxide leaving the lungs after thebreath-hold period corresponds to a continuous outflow from the lungs ofTVCO₂:T₂=14:7=2 ml CO₂/s.

The inflow being larger than the outflow, carbon dioxide is accumulatedin the lungs at the blood/gas barrier during the breath that includesthe breath-hold period. This is confirmed by the increase in theend-tidal CO₂ value P_(et) from 5.0% to 5.5%. The effective lung volumeassociated with this increase of the end-tidal CO₂ value can be calledEVG and is calculated as $\begin{matrix}{{EVG} = {{100 \cdot T_{2}}\quad \frac{\frac{{TVCO2}_{1}}{T_{1}} - \frac{{TVCO2}_{2}}{T_{2}}}{P_{et2} - P_{et1}}}} & (1)\end{matrix}$

If V_(a1) and V_(a2) are substituted for TVCO2₁:T₁ and TVCO2₂:T₂,respectively, as the designations for the average rate of flow of carbondioxide over the durations T₁ and T₂ of the two breaths, Equation (1)can be rewritten as $\begin{matrix}{{EVG} = {{100 \cdot T_{2}}\quad \frac{V_{a1} - V_{a2}}{P_{et2} - P_{et1}}}} & \left( 1^{\prime} \right)\end{matrix}$

EVG=1400 ml in the above example.

Equation (1) or (1′) expresses EVG as a quantity which is proportionalto the ratio of the difference in carbon dioxide flow rates to thedifference in end-tidal carbon dioxide concentrations. It provides asensitive indication of the effective lung volume because virtually nogas mixing takes place during the breath-hold manoeuvre.

EVG is also highly specific for the functional part of the lungs to beexamined, because it does not include contributions from areas of thelungs that are ventilated but not perfused by blood, that is, areaswhere no carbon dioxide is released and, consequently, no contributionis made to the increase in the end-tidal carbon dioxide level P_(et).Areas that have very little or no ventilation will not contributeeither, because in these areas equilibrium between the carbon dioxidepartial pressures in the blood and in the gas phase has been reached sothat no carbon dioxide will pass through the blood/gas barrier.

Thus, EVG is a specific as well as sensitive measure of the functionalpart of the lungs in which the gas exchange is efficient.

It should be noted that in Equation (1) and (1′) the time factor T₂ isincluded in order to provide a quantity EVG the dimension of which isvolume (millilitre). If desired, T₂ can be omitted or replaced with someother time-based proportionality factor, because for practical purposesthe usefulness of EVG resides in changes of EVG values (ΔEVG), ratherthan in the actual numerical EVG values.

It should also be noted that in the EVG determination using Equation (1)as described above, it is possible to base the determination on ameasurement of the oxygen uptake instead of, or in addition to, thecarbon dioxide elimination. The only modification that is required is asubstitution in Equation (1) of the values of the average oxygen flowrate for the values of the average carbon dioxide flow rate. Using thevalues of the average carbon dioxide flow rate is believed normally tobe preferable if EVG determination only is required or desired, but aswill become apparent below, EVG determination on the basis of the valuesof the average oxygen flow may also be useful.

The usefulness of the present invention, can be illustrated by referenceto the well established clinical procedure in which the lungs issubjected to a positive end-expiratory pressure, PEEP, usually expressedin cmH₂O. This can be done by means of any modern ventilator, e.g. byclosing the expiratory breathing line E before completion of theexpiration, thereby trapping some air in the lungs so that the lungsremain somewhat overexpanded at the end of expiration. The elasticmuscle forces acting to restore the original lung volume will thereforeproduce the desired PEEP pressure in the lungs. The compliance(stiffness) C of the lungs is defined in this case by the ratioC=dv:PEEP (ml/cmH₂O) wherein dV is the volume (ml) of air trapped in thelungs.

The same PEEP effect can be achieved in a spontaneously breathing personby introducing a suitable resistance to expiratory flow in theexpiratory breathing line E.

For a patient connected to a ventilator, C can be calculated as$\begin{matrix}{C = \frac{VT}{P_{p} - {PEEP}}} & (2)\end{matrix}$

where P_(p) (pause pressure) is the pressure in the lungs immediatelyprior to the start of expiration. All the parameters in Equation (2) arereadily available from a modern respirator (see FIG. 1). The purpose ofPEEP therapy is to open collapsed lung segments, thereby to provideadditional volumes in the lungs into which gas can enter and thereby toincrease the effective volume for gas exchange. However, producing apressure in the lungs may have negative effects as well. The mostobvious of these is that the pressure will make it more difficult forthe heart to pump blood through the lungs. Pulmonary blood flow maytherefore decrease as a result of the application of PEEP, particularlyin patients with a compromised circulatory state. A reduced blood flowcan then be as detrimental to overall gas exchange as is a smalleffective lung volume. Evaluating PEEP therapy is therefore a highpriority in the treatment of the severely ill patient.

FIG. 3 shows several cases where the new method and apparatus were usedpostoperatively on ventilated patients. Changes in EVG is in all casescompared with the expected mechanical expansion dV of the lungsresulting from increasing PEEP from 0 to 6 cmH₂O.

FIG. 3a shows a case with lungs of normal compliance of about 50(ml/cmH₂O) where EVG increases with the expansion of the lungs as PEEPis increased from 0 to 6 cmH₂O. FIG. 3b shows a stiffer lungs where EVGremains nearly unaffected by the same increase in PEEP, indicating thatthe application of PEEP of this magnitude is of little or no benefit tothe patient. FIG. 3c shows a case where there is an initial significantdecrease in EVG for PEEP=3 cmH₂O followed by an impressive improvementfor PEEP=6 cmH₂O. Finally, FIG. 3d shows a case where PEEP=3 cmH₂Oclearly improves the effective gas exchange volume, but for PEEP=6 cmH₂Othe negative effects of the pressure come into play and virtuallyeliminate the gain seen for PEEP=3 cmH₂O.

As is seen from these examples, one can define a dimensionlessparameter, EG, for the efficiency of gas exchange, which is expected tobe <1 and close to 1 when PEEP therapy works as intended. A therapeuticintervention, i.e. a change in PEEP level (ΔPEEP) can be evaluated bythe change produced in EVG (ΔEVG) by calculating the value of EG fromthe equation $\begin{matrix}{{EG} = {\frac{\Delta \quad {EVG}}{VT} \cdot \frac{P_{p} - {PEEP}}{\Delta \quad {PEEP}}}} & (3)\end{matrix}$

All parameters in Equation (3) can be easily measured noninvasively inthe clinical setting.

Naturally, it is possible to determine EVG for different breath-holdtimes. FIG. 4 illustrates an example in which EVG has been determinedaccording to Equation (1) or (1′) for breath-hold times T_(b) 3 secondsand 6 seconds.

Assuming that these breath-hold times are so short that there is noappreciable effect on the steady state carbon dioxide elimination, atleast in the effective parts of the lungs, the change of the EVG withtime can be treated as a linear process. Accordingly, the amount ofcarbon dioxide leaving the pulmonary blood can be regarded asproportional to the difference between the carbon dioxide partialpressure in the gas phase and that in the blood. It is thereforepossible to extrapolate the EVG linearly back to T_(b)=0 as is indicatedby the broken line in FIG. 4. Since it is known that it takes 0.5seconds for carbon dioxide to reach equilibrium with lung tissue andpulmonary blood (R. Hyde et al: “Rate of Disappearance of Labeled Carbondioxide from the Lungs of Human Beings during Breath Holding . . . ”,The Journal of Clinical Investigation, Vol. 47, 1968, pp 1535-1552), theextrapolated EVG value for T_(b)=0 can be taken as a representation ofonly the tissue phase portion, V_(t), plus the blood compartmentportion, V_(b) of the EVG.

Thus, the lung tissue volume, V_(t), can be estimated from the EVGvalue, EVG₆, for T_(b)=6 seconds using the following equation

V _(t) =EVG ₆ −V _(g) −V _(b)  (4)

From FIG. 4 it is seen that V_(t)+V_(g)=1030 ml in the illustratedexemplary case. Moreover, since the pulmonary blood volume, V_(b), isnormally only about 90 ml (R. Hyde et al: “Rate of Disappearance ofLabeled Carbon dioxide from the Lungs of Human Beings during BreathHolding . . . ”, The Journal of Clinical Investigation, Vol. 47, 1968,pp 1535-1552), an approximate value of V_(t) can be obtained using theequation V_(t)=EVG₆−V_(g)90. Accordingly, in the exemplary case of FIG.4, V_(t) is approximately 940 ml.

In patients suffering from certain lung diseases, such as pulmonaryedema and emphysema, the lung tissue volume is severely affected.Consequently, the method according to the invention as described withreference to FIG. 4 provides an indicator which is useful in monitoringand/or assessing therapy.

As is appreciated from the description of FIG. 4, the method fordetermining V_(t) is based on the assumption that the change of EVG withtime is sufficiently linear-to admit of a linear approximation.Actually, the change is non-linear, however, and the usefulness of themethod therefore is limited to those instances in which a linearapproximation produces results which are useful in spite of theinaccuracy caused by the nonlinearity of the EVG change with time.

An alternative, and more accurate, method for determining V_(t) inaccordance with the invention will now be described.

According to Hyde et al (cited above), carbon dioxide is equilibratedwith lung tissue and capillary blood in about 0.5 s. Hence, the combinedlung tissue and pulmonary blood volumes can be calculated, usingEquation (1) and setting T2=T_(b)+0,5: $\begin{matrix}{{V_{t} + V_{b}} = {100 \cdot \left( {T_{b} + 0.5} \right) \cdot \frac{V_{a1} - V_{a2}}{P_{et2} - P_{et12}}}} & (5)\end{matrix}$

The total volume of carbon dioxide, including the volume resulting fromthe slow diffusion into gas and tissue compartments, can be calculatedaccording to Hyde et al: $\begin{matrix}{V_{Tot} = \frac{EVG}{1 - {0.55 \cdot ^{{- 0.725} \cdot {Qp} \cdot {T2}}}}} & (6)\end{matrix}$

in which Qp is the pulmonary blood flow in liters per second and T2 ismeasured in seconds.

The gas compartment volume is V_(g)=V_(TOt)−(V_(t)+V_(b)), and becauseV_(b) is almost constant and small, about 90 ml, V_(Tot) for a patientwith Qp equal to, say, 0.067 l/s can be calculated from Equation (6):2300 ml.

From Equation (5) it is seen that V_(t)+V_(b)=700 ml, and with V_(b)=90ml, V_(t) will be=610. Finally, the gas compartment volumeV_(g)=2300−1030=1270 ml.

It is important to note that it is also possible to determine the tissuevolume, V_(t), using EVG as measured by means of the oxygen uptake inthe lung instead of by means of carbon dioxide elimination as describedabove. Equation (1) can be used, but instead of inserting the values ofthe carbon dioxide flows, the values of the oxygen inflow are used, andmoreover the end-tidal values to be used are those for the oxygenpartial pressures. Both the nominator and the denominator will changesigns compared with the case where carbon dioxide values are used, andthe EVG value will thus remain positive. Oxygen does not dissolve inpulmonary tissue, and the entire EVG value for oxygen, EVG_(O2),measured in this way is therefore associated with V_(g). Ignoring theinsignificant difference between the volumes of CO₂ and O₂ dissolved inthe blood, the following relationship applies:

V _(t) =EVG _(CO2) −EVG _(O2)  (7)

What is claimed is:
 1. A method for determining a pulmonary functionparameter, EVG, indicative of a living subject's effective lung volume,namely the lung volume in which gas exchange between respiratory air andpulmonary blood takes place efficiently, comprising the steps ofdetermining for a first breath during normal steady state breathing ofthe subject the end-tidal concentration P_(et1) of a given component ofthe respiratory air, said given component being one of carbon dioxideand oxygen, and the average rate of flow V_(a1), over the duration T₁ ofthe breath, of the quantity of said given component expired during thebreath, determining for a second breath comprising a breath-hold periodthe end-tidal concentration P_(et2) of said given component and theaverage rate of flow V_(a2), over the duration T₂ of the breath, of thequantity of said given component expired during the breath, determiningEVG as a quantity proportional to the ratio of the difference betweensaid average flow rates V_(a1) and V_(a2) of said given component to thedifference between said end-tidal concentrations P_(et2) and P_(et1) ofsaid given component.
 2. A method according to claim 1 in which thebreath-hold period separates the inspiration and the expiration of thesecond breath.
 3. A method according to claim 1 in which the breath-holdperiod precedes the inspiration of the second breath.
 4. A methodaccording to claim 1 in which the duration of the breath-hold period is1 to 15 seconds.
 5. A method according to claim 1 in which the step ofdetermining EVG is carried out using the equation $\begin{matrix}{{EVG} = {{100 \cdot T_{2}}\quad \frac{\left( {V_{a1} - V_{a2}} \right)}{\left( {P_{et2} - P_{et1}} \right)}}} & \left( 1^{\prime} \right)\end{matrix}$

in which V_(a1), V_(a2), P_(et1), P_(et2) and T₂ are the same quantitiesas above.
 6. A method according to claim 1 in which the subject breathesspontaneously.
 7. A method according to claim 1 in which the subjectbreathes with the aid of a ventilator.
 8. A method according to claim 1which comprises the additional step of determining the change of thesubject's EVG as a function of positive end-expiratory pressure, PEEP,of the subject's lungs.
 9. A method for determining lung tissue volume,V_(t), of a living subject, comprising the steps of determining thevalues of the subject's EVG in accordance with claim 1 for two differentnon-zero breath-hold durations, determining by linear extrapolation fromthe EVG values so determined a value of the subject's EVG for zerobreath-hold duration, and determining the V_(t) of the subject from theknown relationship of V_(t) to said EVG value for zero breath-holdduration and the EVG value for a non-zero breath-hold duration.
 10. Amethod for determining lung tissue volume, V_(t), of a living subject,comprising the steps of determining the value, EVG_(CO2), of thesubject's EVG in accordance with claim 1 using carbon dioxide as saidgiven component of the respiratory gas, determining the value,EVG_(CO2), of the subject's EVG in accordance with claim 1 using oxygenas said given component of the respiratory gas, determining V_(t) fromthe equation V _(t) =EVG _(CO2) −EVG _(O2)  (7).
 11. A device fordetermining a pulmonary function parameter, EVG, indicative of a livingsubject's effective lung volume, namely the lung volume in which gasexchange between respiratory air and pulmonary blood takes placeefficiently, comprising means for determining for a first breath duringnormal steady state breathing of the subject the end-tidal concentrationP_(et1) of a given component of the respiratory gas, said givencomponent being one of carbon dioxide and oxygen, and the average rateof flow V_(a1), over the duration T₁ of the breath, of the amount ofsaid given component expired during the breath, means for determiningfor a second breath comprising a breath-hold period the end-tidalconcentration P_(et2) of said given component and the average rate offlow V_(a2), over the duration T₂ of the breath, of the amount of saidgiven component expired, means for determining EVG as a quantityproportional to the ratio of the difference between said average flowrates V_(a1), and V_(a2) to the difference between said end-tidalconcentrations P_(et2) and P_(et1).
 12. Apparatus according to claim 11including means for determining EVG using the equation $\begin{matrix}{{EVG} = {{100 \cdot T_{2}}\quad \frac{\left( {V_{a1} - V_{a2}} \right)}{\left( {P_{et2} - P_{et1}} \right)}}} & \left( 1^{\prime} \right)\end{matrix}$

in which V_(a1), V_(a2), P_(et2), P_(et2) and T₂ are the same quantitiesas above.
 13. Apparatus according to claim 11 including means fordetermining the change, ΔEVG, of the subject's EVG as a function ofpositive end-expiratory pressure, PEEP, of the lungs